I rode down to Stanford last night, to catch Wolfram's follow-up lecture tour to A New Kind of Science. A beautiful, over-capacity auditorium, filled with mostly male, compsci/math/physics types, from wide-eyed "math is better than lsd" fan-boys, to more sceptical and reserved grey beards.

Wolfram's lecture was a one-hour version of ANKOS. And it was surprisingly lucid -- for me at least, since I've actually read it (At one point Wolfram praised his readers, especially some masochists who read it 2 or 3 times!). He's not exactly the most engaging speaker, but most everyone felt obliged to pay keen attention for an hour, considering Wolfram spent 10 years staring at cellular automata. He used his hands a lot - mostly a kind of chop, but every so often a forward thrust Wave. Most of his concessions to engagement and laughter came from numerous plugs for Mathematica. Another hearty response came as he described proof-reading the first print ANKOS, and discovering a one pixel error on page 157 -- discovered to be a long time bug in PostScript. Yes, this was a PostScript joke loving crowd.

He made a striking image, standing in front of a screen four times his height, fantastic cascading cellular automata, his genius large and precise and illuminated. At one point he displayed the figure from p. 773 of ANKOS, Axiom systems for traditional mathematics, by saying, very offhandedly, "And here is the foundation of all present day mathematics", and following it up with his enumeration of every possible mathematics. He is no doubt Brilliant, very Brilliant, a master of numerous sciences. It's a Brilliance of Exposition & Methodology. The accumulated weight of his words accounts for the fan-boy awe, definitely not the brilliance of Brevity. His Principle of Computational Irreducability :: that some processes in nature can not be reduced to formula, the simplest "solution" being only to let the process run its course :: definitely applies to Wolfram! His expoundings are not reduced at all!

He sees his work as a huge Paradigm Shift in Science. I see it more as a political grab to harness many already existing streams of thought in Science. He wishes to create a Framework for Science to operate in :: in other words, in Science, we'd all be doing tasks on his behalf. It's impossible to Lead the Paradigm Shift in Science resulting from Computation, We all must be fully participating in the excitement of the Mysteries.

His original work is striking, expecially the methodology :: ofr example, he was able to find the as yet simplest Universal Turing Machine, just by enumerating through Turing Machines for one that displayed "Class 4" behavior. But much of ANKOS is reformulations and conjectures.

One question from the audience was "How do you know Rule 30 is not eventually periodic?", and he could only answer that he'd really like to have a proof. This would be a major result! The first audience question :: "How do you account for your intellectual structure nor representing Reality?" :: really flustered Wolfram, and got a huge laugh. Still, some fanboys asked guru-type questions like "What is the fundemental nature of reality", expecting an answer. During the Q/A, Wolfram suddenly appeared a lot more human.

I have two main problems with ANKOS. First, the section on examples, especially in the Biological Sciences, was quite lean. Philip Ball in The Self-Made Tapestry: Pattern Formation in Nature goes into much greated detail. Second, he misses a basic point with the Principle of Computational Equivalence. In his Universal Cellular Automaton, he argues it is as powerful as any other CA, since it is only dependent on initial conditions to emulate another rule -- or there's no added complexity beyond the underlying rule. Any first year computer science student knows that there is no difference between Program and Data. Wolfram ignores the Encoding of the problem in the higher level complexity of his Universal CA, disregarding Emergence, and in essence trotting out a new type of Reductionism.

As you can see, it was great, very stimulating! I'm looking forward to reentering academics next year.